a.c

#include <stdio.h>
#include <stdlib.h>

struct Xs {
    int x[32];
    int y[32];
};

void print(int n, struct Xs *pX)
{
    int i, len;
    char *p, buf[4096];

    len = sprintf(buf, "x%d = ", n);
    p = buf + len;
    for (i = 0; i < 32; i++)
    {
        if (pX->y[i])
        {
            len = sprintf(p, "y%d ^ ", i);
            p += len;
        }
    }
    for (i = 0; i < 32; i++)
    {
        if (pX->x[i])
        {
            len = sprintf(p, "x%d ^ ", i);
            p += len;
        }
    }
    *(p-3) = '\0';
    puts(buf);
}

int main()
{
    int i, j, k, flag;
    struct Xs X[32];

    memset(X, 0, sizeof(X));
    for (i = 0; i < 32; i++)
    {
        X[i].y[i] = 1;
        j = (i + 8) % 32;
        k = (i + 7) % 32;
        X[i].x[j] = 1;
        X[i].x[k] = 1;
    }
    while (1)
    {
        flag = 0;
        for (i = 0; i < 32; i++)
        {
            for (j = 0; j < 32; j++)
            {
                if (j == i)
                    continue;
                if (X[i].x[j])
                {
                    flag = 1;
                    X[i].x[j] = 0;
                    for (k = 0; k < 32; k++)
                    {
                        if (X[j].y[k])
                            X[i].y[k] ^= X[j].y[k];
                    }
                    for (k = 0; k < 32; k++)
                    {
                        if (X[j].x[k])
                            X[i].x[k] ^= X[j].x[k];
                    }
//                  print(i, &X[i]);
                }
            }
        }
        if (flag == 0)
            break;
    }

    printf("---\n");
    for (i = 0; i < 32; i++)
        print(i, &X[i]);
    printf("---\n");

    return 0;
}